Ab Initio Quantum Chemical Investigation of the Spin States of Some Fused Ring Systems

The ground-state spins of seven diradicals belonging to the fused ring system have been investigated by ab
initio restricted and unrestricted formalisms. The systems under study are (<b>1</b>) 4-oxy-2-naphthalenyl methyl,
(<b>2</b>) 1,8-naphthalenediylbis(methyl), (<b>3</b>) 8-imino-1-naphthalenyl methyl, (<b>4</b>) 1,8- naphthalenediylbis(amidogen),
(<b>5</b>) 8-methyl-1-naphthyl carbene, (<b>6</b>) 8-methyl-1-naphthalenyl imidogen, and (<b>7</b>) 8-methyl-1-naphthyl
diazomethane. Out of the seven molecules, only <b>1</b> was theoretically investigated earlier. To our knowledge,
for <b>2</b>−<b>7</b>, this work represents the first ab initio investigation. A variety of basis sets have been employed in
these calculations. For each spin state, the molecular geometry has been fully optimized at the unrestricted
Hartree−Fock (UHF) level using the STO-3G, 4-31G, 6-311G(d), and 6-311G(d,p) basis sets. The UHF
optimized geometries have been used for Møller−Plesset (MP) and coupled cluster (CC) calculations as well
as the density functional (UB3LYP) treatment. Results in the unrestricted formalism have been given only at
UHF and UB3LYP levels for the 6-311G(d) basis. The UHF calculations yield an unrealistically large singlet−triplet (S−T) splitting. Splittings calculated with different bases disagree seriously. The S−T gap is smaller
in the split-valence bases. The basis set truncation error can be considerably overcome by calculations involving
electron correlation. For these diradicals, any meaningful result would require larger bases with polarization
functions. Apart form this difficulty, the optimized geometry turned out to be highly spin-contaminated. The
spin-contamination can be significantly reduced by the density functional UB3LYP treatment. Nevertheless,
for most of the diradicals, the UB3LYP method did not yield a systematic trend. To avoid spin contamination
completely, we have repeated computations in the restricted (open-shell) Hartree−Fock framework. Geometry
optimizations were carried out using STO-3G, 6-311G(d), and 6-311G(d,p) bases at the R(O)HF level and
6-311G(d,p) basis at the R(O)B3LYP level for each spin state. The R(O)B3LYP/6-311G(d,p) optimized
geometry yields the best total energy for each spin state and hence the most reliable S−T energy difference.
Molecules <b>1</b>−<b>6</b> are found as ground-state triplets. The calculated results are in agreement with the available
experimental findings. Molecules <b>3</b> and <b>7 </b>have widely different geometries in the singlet and triplet states.
The calculations using 6-311G(d) and 6-311G(d,p) basis sets show that in molecule <b>3 </b>the substituents of
naphthalene are −NH<sub>2</sub> and −CH in singlet but −NH and −CH<sub>2</sub> in triplet. The two optimized geometries are
tautomeric forms. Molecule <b>7</b> is expected to be either a ground-state triplet with a very little S−T gap or a
ground-state singlet. This prediction is borne out by the computed results. The R(O)B3LYP/6-311G(d,p)
calculation yields a S−T splitting of −21.9 kcal mol<sup>-1</sup>. The singlet state becomes stabilized by forming an
additional condensed ring. The UHF spin density plots obtained from the 4-31G optimized geometries manifest
the phenomenon of spin alternation in the ground state.